Details

analyze1.1s (7.4%)

Algorithm

1×

Search

True	Other	False	Iter
0%	100%	0%	0
0%	100%	0%	1
0%	100%	0%	2
0%	75%	25%	3
0%	62.5%	37.5%	4
0%	56.2%	43.8%	5
3.1%	46.9%	50%	6
3.1%	45.3%	51.6%	7
3.1%	44.5%	52.4%	8
3.5%	44.1%	52.4%	9
3.7%	43.9%	52.4%	10
3.8%	43.8%	52.4%	11
3.8%	43.8%	52.4%	12
3.8%	43.8%	52.4%	13
3.8%	43.7%	52.4%	14

Compiler

Compiled 38 to 31 computations (18.4% saved)

sample226.0ms (1.5%)

Algorithm

1×

intervals

Results

72.0ms	124×	body	1024	valid
63.0ms	116×	body	1024	nan
30.0ms	73×	body	512	valid
21.0ms	57×	body	512	nan
10.0ms	10×	body	2048	valid
9.0ms	31×	body	256	valid
5.0ms	20×	body	256	nan
3.0ms	18×	body	128	valid

Compiler

Compiled 75 to 62 computations (17.3% saved)

simplify271.0ms (1.7%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (93.0ms)

Iter	Nodes	Cost
0	4731	55
1	4731	55

prune20.0ms (0.1%)

Pruning

1 alts after pruning (1 fresh and 0 done)

	Pruned	Kept	Total
New	0	1	1
Fresh	1	0	1
Picked	0	0	0
Done	0	0	0
Total	1	1	2

Merged error: 61.9b

Counts

2 → 1

Compiler

Compiled 133 to 102 computations (23.3% saved)

localize20.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.3b	(*.f64 PI.f64 f)
0.3b	(*.f64 (/.f64 PI.f64 4) f)
0.3b	(*.f64 (/.f64 PI.f64 4) f)
6.6b	(-.f64 (exp.f64 (.f64 (/.f64 PI.f64 4) f)) (pow.f64 (exp.f64 -1/4) (.f64 PI.f64 f)))

rewrite43.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

41×	`add-sqr-sqrt_binary64`
29×	`associate-l_binary64`
26×	`*-un-lft-identity_binary64`
24×	`add-cube-cbrt_binary64`
20×	`times-frac_binary64`
16×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
10×	`pow1_binary64`
9×	`associate-r_binary64`
7×	`cancel-sign-sub-inv_binary64`
6×	`add-log-exp_binary64`
5×	`cbrt-unprod_binary64` `unswap-sqr_binary64` `prod-exp_binary64`
4×	`unpow-prod-down_binary64`
3×	`pow-prod-down_binary64` `difference-of-squares_binary64` `*-commutative_binary64`
2×	`cbrt-undiv_binary64` `sqr-pow_binary64` `div-inv_binary64` `div-exp_binary64` `associate-*l/_binary64`
1×	`sub-neg_binary64` `flip3--_binary64` `diff-log_binary64` `distribute-lft-out--_binary64` `flip--_binary64`

Counts

4 → 104

Calls

4 calls:

9.0ms	(-.f64 (exp.f64 (.f64 (/.f64 PI.f64 4) f)) (pow.f64 (exp.f64 -1/4) (.f64 PI.f64 f)))
8.0ms	(*.f64 (/.f64 PI.f64 4) f)
8.0ms	(*.f64 (/.f64 PI.f64 4) f)
4.0ms	(*.f64 PI.f64 f)

series191.0ms (1.2%)

Counts

4 → 12

Calls

4 calls:

83.0ms	(-.f64 (exp.f64 (.f64 (/.f64 PI.f64 4) f)) (pow.f64 (exp.f64 -1/4) (.f64 PI.f64 f)))
47.0ms	(*.f64 (/.f64 PI.f64 4) f)
36.0ms	(*.f64 (/.f64 PI.f64 4) f)
25.0ms	(*.f64 PI.f64 f)

simplify74.0ms (0.5%)

Algorithm

1×	egg-herbie

Counts

116 → 116

Iterations

Useful iterations: 0 (53.0ms)

Iter	Nodes	Cost
0	4982	1633
1	4982	1633

prune301.0ms (1.9%)

Pruning

2 alts after pruning (1 fresh and 1 done)

	Pruned	Kept	Total
New	115	1	116
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	115	2	117

Merged error: 1.1b

Counts

117 → 2

Compiler

Compiled 5424 to 3662 computations (32.5% saved)

localize42.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.3b	(*.f64 (/.f64 PI.f64 4) f)
0.3b	(.f64 f (.f64 PI.f64 -1/4))
0.3b	(/.f64 (+.f64 (exp.f64 (.f64 (/.f64 PI.f64 4) f)) (pow.f64 (exp.f64 -1/4) (.f64 PI.f64 f))) (+.f64 (.f64 (pow.f64 (.f64 PI.f64 f) 3) 1/384) (+.f64 (.f64 (.f64 PI.f64 f) (+.f64 1/4 (.f64 (.f64 PI.f64 f) 1/32))) (-.f64 (.f64 (pow.f64 (.f64 (/.f64 PI.f64 4) f) 3) 1/6) (+.f64 (.f64 f (.f64 PI.f64 -1/4)) (.f64 1/2 (.f64 (pow.f64 PI.f64 2) (.f64 (.f64 f f) 1/16))))))))
0.4b	(.f64 (log.f64 (/.f64 (+.f64 (exp.f64 (.f64 (/.f64 PI.f64 4) f)) (pow.f64 (exp.f64 -1/4) (.f64 PI.f64 f))) (+.f64 (.f64 (pow.f64 (.f64 PI.f64 f) 3) 1/384) (+.f64 (.f64 (.f64 PI.f64 f) (+.f64 1/4 (.f64 (.f64 PI.f64 f) 1/32))) (-.f64 (.f64 (pow.f64 (.f64 (/.f64 PI.f64 4) f) 3) 1/6) (+.f64 (.f64 f (.f64 PI.f64 -1/4)) (.f64 1/2 (.f64 (pow.f64 PI.f64 2) (.f64 (*.f64 f f) 1/16))))))))) (/.f64 -4 PI.f64))

rewrite79.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

40×	`add-sqr-sqrt_binary64`
38×	`*-un-lft-identity_binary64`
32×	`times-frac_binary64`
30×	`add-cube-cbrt_binary64`
21×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
20×	`associate-l_binary64`
17×	`associate-r_binary64`
14×	`pow1_binary64`
7×	`cbrt-unprod_binary64` `prod-exp_binary64`
5×	`pow-prod-down_binary64`
4×	`add-log-exp_binary64` `distribute-lft-out_binary64` `unswap-sqr_binary64` `associate-/l*_binary64`
3×	`associate-/r_binary64` `cbrt-undiv_binary64` `div-inv_binary64` `div-exp_binary64` `-commutative_binary64`
2×	`flip3-+_binary64` `associate-/l/_binary64` `associate-/r/_binary64` `flip-+_binary64`
1×	`associate-r/_binary64` `log-pow_binary64` `clear-num_binary64` `frac-2neg_binary64` `associate-l/_binary64`

Counts

4 → 118

Calls

4 calls:

30.0ms	(/.f64 (+.f64 (exp.f64 (.f64 (/.f64 PI.f64 4) f)) (pow.f64 (exp.f64 -1/4) (.f64 PI.f64 f))) (+.f64 (.f64 (pow.f64 (.f64 PI.f64 f) 3) 1/384) (+.f64 (.f64 (.f64 PI.f64 f) (+.f64 1/4 (.f64 (.f64 PI.f64 f) 1/32))) (-.f64 (.f64 (pow.f64 (.f64 (/.f64 PI.f64 4) f) 3) 1/6) (+.f64 (.f64 f (.f64 PI.f64 -1/4)) (.f64 1/2 (.f64 (pow.f64 PI.f64 2) (.f64 (.f64 f f) 1/16))))))))
9.0ms	(.f64 (log.f64 (/.f64 (+.f64 (exp.f64 (.f64 (/.f64 PI.f64 4) f)) (pow.f64 (exp.f64 -1/4) (.f64 PI.f64 f))) (+.f64 (.f64 (pow.f64 (.f64 PI.f64 f) 3) 1/384) (+.f64 (.f64 (.f64 PI.f64 f) (+.f64 1/4 (.f64 (.f64 PI.f64 f) 1/32))) (-.f64 (.f64 (pow.f64 (.f64 (/.f64 PI.f64 4) f) 3) 1/6) (+.f64 (.f64 f (.f64 PI.f64 -1/4)) (.f64 1/2 (.f64 (pow.f64 PI.f64 2) (.f64 (*.f64 f f) 1/16))))))))) (/.f64 -4 PI.f64))
8.0ms	(*.f64 (/.f64 PI.f64 4) f)
6.0ms	(.f64 f (.f64 PI.f64 -1/4))

series1.1s (7.4%)

Counts

4 → 12

Calls

4 calls:

859.0ms	(.f64 (log.f64 (/.f64 (+.f64 (exp.f64 (.f64 (/.f64 PI.f64 4) f)) (pow.f64 (exp.f64 -1/4) (.f64 PI.f64 f))) (+.f64 (.f64 (pow.f64 (.f64 PI.f64 f) 3) 1/384) (+.f64 (.f64 (.f64 PI.f64 f) (+.f64 1/4 (.f64 (.f64 PI.f64 f) 1/32))) (-.f64 (.f64 (pow.f64 (.f64 (/.f64 PI.f64 4) f) 3) 1/6) (+.f64 (.f64 f (.f64 PI.f64 -1/4)) (.f64 1/2 (.f64 (pow.f64 PI.f64 2) (.f64 (*.f64 f f) 1/16))))))))) (/.f64 -4 PI.f64))
206.0ms	(/.f64 (+.f64 (exp.f64 (.f64 (/.f64 PI.f64 4) f)) (pow.f64 (exp.f64 -1/4) (.f64 PI.f64 f))) (+.f64 (.f64 (pow.f64 (.f64 PI.f64 f) 3) 1/384) (+.f64 (.f64 (.f64 PI.f64 f) (+.f64 1/4 (.f64 (.f64 PI.f64 f) 1/32))) (-.f64 (.f64 (pow.f64 (.f64 (/.f64 PI.f64 4) f) 3) 1/6) (+.f64 (.f64 f (.f64 PI.f64 -1/4)) (.f64 1/2 (.f64 (pow.f64 PI.f64 2) (.f64 (.f64 f f) 1/16))))))))
40.0ms	(.f64 f (.f64 PI.f64 -1/4))
39.0ms	(*.f64 (/.f64 PI.f64 4) f)

simplify120.0ms (0.8%)

Algorithm

1×	egg-herbie

Counts

130 → 130

Iterations

Useful iterations: 0 (40.0ms)

Iter	Nodes	Cost
0	5182	10374

prune977.0ms (6.3%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	122	8	130
Fresh	0	0	0
Picked	1	0	1
Done	0	1	1
Total	123	9	132

Merged error: 0.5b

Counts

132 → 9

Compiler

Compiled 19566 to 13095 computations (33.1% saved)

localize36.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.3b	(.f64 f (.f64 PI.f64 -1/4))
0.3b	(-.f64 (+.f64 (.f64 1/96 (.f64 PI.f64 (.f64 f f))) (+.f64 (.f64 1/4 (.f64 f (.f64 f (.f64 PI.f64 -1/4)))) (.f64 4 (/.f64 (log.f64 f) PI.f64)))) (+.f64 (.f64 1/2 (.f64 PI.f64 (.f64 (.f64 f f) 1/16))) (+.f64 (.f64 f -1/2) (+.f64 (.f64 4 (/.f64 (log.f64 (/.f64 4 PI.f64)) PI.f64)) (*.f64 f 1/2)))))
0.3b	(/.f64 (log.f64 f) PI.f64)
2.0b	(log.f64 (/.f64 4 PI.f64))

rewrite72.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

58×	`add-log-exp_binary64`
30×	`sum-log_binary64`
24×	`*-un-lft-identity_binary64` `add-sqr-sqrt_binary64`
22×	`add-cube-cbrt_binary64`
21×	`times-frac_binary64`
14×	`pow1_binary64` `add-exp-log_binary64`
13×	`log-prod_binary64`
12×	`diff-log_binary64`
11×	`add-cbrt-cube_binary64`
5×	`log-pow_binary64`
4×	`flip3-+_binary64` `associate-/l*_binary64` `flip-+_binary64` `frac-sub_binary64`
3×	`pow-prod-down_binary64` `associate-/r_binary64` `cbrt-unprod_binary64` `associate-l*_binary64` `cancel-sign-sub-inv_binary64` `prod-exp_binary64`
2×	`rem-log-exp_binary64` `div-inv_binary64` `div-exp_binary64`
1×	`sub-neg_binary64` `associate--r+_binary64` `flip3--_binary64` `associate-r_binary64` `cbrt-undiv_binary64` `clear-num_binary64` `frac-2neg_binary64` `difference-of-squares_binary64` `distribute-lft-out--_binary64` `log-div_binary64` `flip--_binary64` `associate--l+_binary64` `*-commutative_binary64`

Counts

4 → 106

Calls

4 calls:

39.0ms	(-.f64 (+.f64 (.f64 1/96 (.f64 PI.f64 (.f64 f f))) (+.f64 (.f64 1/4 (.f64 f (.f64 f (.f64 PI.f64 -1/4)))) (.f64 4 (/.f64 (log.f64 f) PI.f64)))) (+.f64 (.f64 1/2 (.f64 PI.f64 (.f64 (.f64 f f) 1/16))) (+.f64 (.f64 f -1/2) (+.f64 (.f64 4 (/.f64 (log.f64 (/.f64 4 PI.f64)) PI.f64)) (*.f64 f 1/2)))))
6.0ms	(.f64 f (.f64 PI.f64 -1/4))
4.0ms	(/.f64 (log.f64 f) PI.f64)
3.0ms	(log.f64 (/.f64 4 PI.f64))

series668.0ms (4.3%)

Counts

4 → 10

Calls

4 calls:

506.0ms	(-.f64 (+.f64 (.f64 1/96 (.f64 PI.f64 (.f64 f f))) (+.f64 (.f64 1/4 (.f64 f (.f64 f (.f64 PI.f64 -1/4)))) (.f64 4 (/.f64 (log.f64 f) PI.f64)))) (+.f64 (.f64 1/2 (.f64 PI.f64 (.f64 (.f64 f f) 1/16))) (+.f64 (.f64 f -1/2) (+.f64 (.f64 4 (/.f64 (log.f64 (/.f64 4 PI.f64)) PI.f64)) (*.f64 f 1/2)))))
122.0ms	(/.f64 (log.f64 f) PI.f64)
39.0ms	(.f64 f (.f64 PI.f64 -1/4))
0.0ms	(log.f64 (/.f64 4 PI.f64))

simplify81.0ms (0.5%)

Algorithm

1×	egg-herbie

Counts

116 → 116

Iterations

Useful iterations: 0 (32.0ms)

Iter	Nodes	Cost
0	4986	5351
1	4986	5351

prune1.1s (7.3%)

Pruning

13 alts after pruning (12 fresh and 1 done)

	Pruned	Kept	Total
New	108	8	116
Fresh	3	4	7
Picked	1	0	1
Done	0	1	1
Total	112	13	125

Merged error: 0.5b

Counts

125 → 13

Compiler

Compiled 26639 to 17667 computations (33.7% saved)

localize15.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.2b	(.f64 PI.f64 (.f64 f f))
0.3b	(-.f64 (/.f64 (log.f64 f) PI.f64) (/.f64 (log.f64 (/.f64 4 PI.f64)) PI.f64))
0.3b	(/.f64 (log.f64 f) PI.f64)
2.0b	(log.f64 (/.f64 4 PI.f64))

rewrite50.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

61×	`times-frac_binary64`
51×	`*-un-lft-identity_binary64`
50×	`add-sqr-sqrt_binary64`
37×	`add-cube-cbrt_binary64`
29×	`pow1_binary64`
20×	`log-pow_binary64`
16×	`cancel-sign-sub-inv_binary64`
14×	`add-exp-log_binary64`
13×	`log-prod_binary64` `distribute-lft-out--_binary64`
11×	`add-cbrt-cube_binary64`
6×	`add-log-exp_binary64`
5×	`div-inv_binary64`
4×	`difference-of-squares_binary64` `associate-/l*_binary64`
3×	`pow-prod-down_binary64` `associate-/r_binary64` `cbrt-unprod_binary64` `associate-l*_binary64` `prod-exp_binary64`
2×	`rem-log-exp_binary64` `div-exp_binary64` `log-div_binary64`
1×	`sub-neg_binary64` `flip3--_binary64` `diff-log_binary64` `associate-r_binary64` `distribute-rgt-out--_binary64` `cbrt-undiv_binary64` `associate--r-_binary64` `unswap-sqr_binary64` `div-sub_binary64` `clear-num_binary64` `frac-2neg_binary64` `sub-div_binary64` `flip--_binary64` `frac-sub_binary64` `*-commutative_binary64`

Counts

4 → 122

Calls

4 calls:

21.0ms	(-.f64 (/.f64 (log.f64 f) PI.f64) (/.f64 (log.f64 (/.f64 4 PI.f64)) PI.f64))
6.0ms	(.f64 PI.f64 (.f64 f f))
4.0ms	(/.f64 (log.f64 f) PI.f64)
3.0ms	(log.f64 (/.f64 4 PI.f64))

series392.0ms (2.5%)

Counts

4 → 10

Calls

4 calls:

249.0ms	(-.f64 (/.f64 (log.f64 f) PI.f64) (/.f64 (log.f64 (/.f64 4 PI.f64)) PI.f64))
110.0ms	(/.f64 (log.f64 f) PI.f64)
33.0ms	(.f64 PI.f64 (.f64 f f))
0.0ms	(log.f64 (/.f64 4 PI.f64))

simplify98.0ms (0.6%)

Algorithm

1×	egg-herbie

Counts

132 → 132

Iterations

Useful iterations: 0 (70.0ms)

Iter	Nodes	Cost
0	4878	2165
1	4878	2165

prune770.0ms (5%)

Pruning

13 alts after pruning (12 fresh and 1 done)

	Pruned	Kept	Total
New	122	10	132
Fresh	9	2	11
Picked	1	0	1
Done	0	1	1
Total	132	13	145

Merged error: 0.5b

Counts

145 → 13

Compiler

Compiled 18988 to 12276 computations (35.3% saved)

regimes51.0ms (0.3%)

Compiler: Compiled 518 to 362 computations (30.1% saved)

bsearch0.0ms (0%)

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	29	32
1	29	32

end0.0ms (0%)

sample7.5s (48.3%)

Algorithm

1×

intervals

Results

2.1s	3805×	body	1024	valid
2.0s	3845×	body	1024	nan
796.0ms	2024×	body	512	valid
695.0ms	1889×	body	512	nan
619.0ms	531×	body	2048	valid
277.0ms	1024×	body	256	valid
245.0ms	997×	body	256	nan
91.0ms	616×	body	128	valid
1.0ms	1×	body	2048	nan
0.0ms	1×	body	128	nan
0.0ms	1×	body	128	overflowed

Compiler

Compiled 573 to 407 computations (29% saved)

Details

analyze1.1s (7.4%)

sample226.0ms (1.5%)

simplify271.0ms (1.7%)

prune20.0ms (0.1%)

localize20.0ms (0.1%)

rewrite43.0ms (0.3%)

series191.0ms (1.2%)

simplify74.0ms (0.5%)

prune301.0ms (1.9%)

localize42.0ms (0.3%)

rewrite79.0ms (0.5%)

series1.1s (7.4%)

simplify120.0ms (0.8%)

prune977.0ms (6.3%)

localize36.0ms (0.2%)

rewrite72.0ms (0.5%)

series668.0ms (4.3%)

simplify81.0ms (0.5%)

prune1.1s (7.3%)

localize15.0ms (0.1%)

rewrite50.0ms (0.3%)

series392.0ms (2.5%)

simplify98.0ms (0.6%)

prune770.0ms (5%)

regimes51.0ms (0.3%)

bsearch0.0ms (0%)

simplify3.0ms (0%)

end0.0ms (0%)

sample7.5s (48.3%)

Profiling